2009 AMC 10B Problems/Problem 2

Problem

Which of the following is equal to $\dfrac{\frac{1}{3}-\frac{1}{4}}{\frac{1}{2}-\frac{1}{3}}$ ?

$\text{(A) } \frac 14 \qquad \text{(B) } \frac 13 \qquad \text{(C) } \frac 12 \qquad \text{(D) } \frac 23 \qquad \text{(E) } \frac 34$

Solution

Multiplying the numerator and the denominator by the same value does not change the value of the fraction. We can multiply both by $12$ , getting $\dfrac{4-3}{6-4} = \boxed{\dfrac 12}$ .

Alternately, we can directly compute that the numerator is $\dfrac 1{12}$ , the denominator is $\dfrac 16$ , and hence their ratio is $\boxed{(C)\frac {1} {2}}$ .

2009 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AMC 10 Problems and Solutions

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2009 AMC 10B Problems/Problem 2

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